Table 3 

Example of calculations from data in Baker and Lindeman [Reference 9] 

hospital 
before" group data 
after group data 
estimate 
std error 
weight 



n1 
e1 
P1 
n2 
e2 
p2 
y 
s 
w 



1 
116 
.586 
.172 
103 
.223 
.184 
.033 
.143 
44 
2 
180 
.290 
.080 
180 
.440 
.090 
.067 
.196 
24 
3 
373 
.131 
.110 
421 
.587 
.100 
.022 
.048 
208 
4 
1000 
.100 
.040 
1000 
.450 
.050 
.029 
.026 
313 
5 
1298 
.000 
.074 
1084 
.480 
.065 
.019 
.022 
333 
6 
1919 
.000 
.275 
2073 
.316 
.229 
.146 
.044 
225 
7 
3195 
.010 
.030 
3733 
.290 
.031 
.004 
.015 
365 
8 
4778 
.008 
.194 
4859 
.586 
.190 
.006 
.014 
369 
9 
4685 
.187 
.149 
6170 
.551 
.125 
.046 
.015 
352 
10 
8108 
.467 
.248 
9918 
.678 
.280 
.152 
.031 
288 
11 
11159 
.328 
.209 
11869 
.499 
.209 
.000 
.031 
288 


n1 (n2) = number of subjects in "before" ("after") group. el (e2) = fraction of subjects in "before" ("after") group that had epdiural analgesia, p1 (p2) = fraction of subjects in "before" ("after") group that had a Cesarean section, y= estimated effect of epidural analgesia on the probability of Cesarean section = (p2p1)/(e2e1), s= standard error of y= square root of (p2 (1p2))/n2 + p1 (1p1)/n1) /(e2e1)^{2}, w^{*} = weight used in random effects metaanalysis. We computed the weights as follows. Let i index studies, so y_{i} and s_{i} are the values of y and s for study i. It is convenient to define w_{1} = I/ s_{i}^{2}. Following DerSimonian and Laird [Reference 19], to compute v, the variance of the true effect among the k studies, we set v equal to the larger of (Q(k1)) / (Σw_{i}  Σw_{i}^{2}/Σw_{i}) and 0, where Q = Σw_{i} (y_{i}  m)^{2}, m = Σy_{i} w_{i}/Σw_{i}. The randomeffects weights are w^{*}_{i}= 1/(s_{i}^{2} + v), and the summary statistic is y^{*} = Σy_{i} w^{*}_{i}/Σw^{*}_{i}, with standard error s^{*} = square root of 1/Σw^{*}_{i}. Following Proschan and Follman [reference 20], the 95% confidence interval is (y^{*}  t_{k} s^{*}, y^{*}+ t_{k1} s^{*}), where t_{k1} is the value of the 97 ½ percentile of a tdistribution with k1 degrees of freedom. In this example, k = 11, Q = 50.1, v = .0025, m =.007, s^{*} = .019 y^{*} = .005, t_{10} = 2.23, y^{*} = .005 and the 95% confidence interval is (.047, .037). 

Baker et al. BMC Medical Research Methodology 2001 1:9 doi:10.1186/1471228819 